Given an m-dimensional compact submanifold M of Euclidean space Rs, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general Rs-valued functionals including median location, which is derived from the spatial median. The asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated. Convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus. An application is given in the context of independent, but not identically distributed, samples, in particular, to a multisample setup.
Publié le : 2007-02-14
Classification:
Compact submanifold of Euclidean space,
cutlocus,
sphere,
Stiefel manifold,
Weingarten mapping,
mean location,
spatial median,
median location,
spherical distribution,
multivariate Lindeberg condition,
stabilization,
confidence region,
62H11,
62G10,
62G15,
53A07
@article{1181100183,
author = {Hendriks, Harrie and Landsman, Zinoviy},
title = {Asymptotic data analysis on manifolds},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 109-131},
language = {en},
url = {http://dml.mathdoc.fr/item/1181100183}
}
Hendriks, Harrie; Landsman, Zinoviy. Asymptotic data analysis on manifolds. Ann. Statist., Tome 35 (2007) no. 1, pp. 109-131. http://gdmltest.u-ga.fr/item/1181100183/